Date: Wed, 20 Nov 1996 19:15:16 GMT
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<HEAD><TITLE> Gaggle Theory </TITLE></HEAD>
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<H2> Gaggle Theory </H2>


<Strong>Description: </Strong> <Blockquote> Gaggle (and not giggle) is
the pronunciation of the acronym "ggl" for generalized galois
logic. This is an algebraic abstraction that covers most of existing
"natural" logics (classical, modal, intuitionistic, relevant, linear,
BCK, Lambek calculus, etc.). A gaggle is a great generalization of the
ideas of Jonnson and Tarski's "Boolean algebras with operators."
Operators can distribute or co-distribute in various of their places
over either meet or join, and are also required to interact with each
other in a way that generalizes the notions of Galois connection and
residuation. The idea is to give a representation theorem using
"Kripke frames," and to interpret an n-ary operator using a n+1 -
placed accessibility relation, as for example necessity in modal logic
is interpreted using a binary accessibility relation.  While the
original focus was gaggles based on underlying distributive lattices,
the project has been extended to underlying partial orders,
semi-lattices, involuted semi-lattices, and lattices.

 </Blockquote>
<P>

<Strong> Associated Faculty: </Strong>  
Gerard Allwein
<P>

<Strong> Associated Graduate Students: </Strong>  
Steve Crowley (Philosophy)
<P>

<Strong> Affiliated Projects: </Strong> Chrysafis Hartonas (University
of Ioannina, Greece), Greg Restall (Automated Reasoning Project,
Australian National University) <P>

<Strong> Support: </Strong> 
College of Arts and Sciences
<p> 

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